Arithmetic Applications (Level 1): MCQ test, Set 2

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Choose one answer for each question, then check your score at the end. Each correct answer carries 1 mark; there is no negative marking.

A box contains 48 bulbs, out of which 18 are defective. If the ratio of defective bulbs to good bulbs is $x : y$ in simplest form, then $x + y =$
A $8$ B $13$ C $11$ D $48$

Answer and solution

Answer: (A) $8$

$\text{Good bulbs} = 48 - 18 = 30$

$\displaystyle \frac{\text{Defective}}{\text{Good}} = \frac{18}{30} = \frac{3}{5} \Rightarrow x : y = 3 : 5$

$x + y = 3 + 5 = 8$
₹2700 is divided among three persons in the ratio $2 : 3 : 4$ . The second share is
A ₹1200 B ₹600 C ₹300 D ₹900

Answer and solution

Answer: (D) ₹900

Sum of the terms $= 2 + 3 + 4 = 9$

$\displaystyle \text{Second share} = \frac{3}{9} \times 2700 = 900$
In a school library, the ratio of comic books to story books is the same as the ratio of story books to Hindi books. If there are 480 story books and 320 Hindi books, then the number of comic books is
A $640$ B $320$ C $720$ D $800$

Answer and solution

Answer: (C) $720$

$\displaystyle \frac{\text{Comic}}{\text{Story}} = \frac{\text{Story}}{\text{Hindi}} = \frac{480}{320} = \frac{3}{2}$

$\displaystyle \text{Comic books} = 480 \times \frac{3}{2} = 720$
If $x : 18 :: 10 : 45$ , then $x =$
A $25$ B $8$ C $81$ D $4$

Answer and solution

Answer: (D) $4$

Product of means $=$ product of extremes.

$45x = 18 \times 10 \Rightarrow x = 4$
The third proportional to 9 and 12 is
A $16$ B $108$ C $6.75$ D $6\sqrt{3}$

Answer and solution

Answer: (A) $16$

$9 : 12 :: 12 : c \Rightarrow 9c = 12 \times 12$

$\displaystyle c = \frac{144}{9} = 16$
If $\displaystyle \frac{x}{y} = \frac{6}{5}$ , then $\displaystyle \frac{x+y}{y} =$
A $\displaystyle \frac{1}{5}$ B $\displaystyle \frac{6}{5}$ C $\displaystyle \frac{11}{5}$ D $\displaystyle \frac{11}{6}$

Answer and solution

Answer: (C) $\displaystyle \frac{11}{5}$

By componendo, $\displaystyle \frac{x+y}{y} = \frac{6 + 5}{5} = \frac{11}{5}$
A pole 12 m high casts a shadow of 8 m. Under similar conditions, a tree that casts a shadow of 14 m is
A $\displaystyle 6\frac{6}{7}$ m high B $18$ m high C $\displaystyle 9\frac{1}{3}$ m high D $21$ m high

Answer and solution

Answer: (D) $21$ m high

Direct proportion: $x_1 y_2 = x_2 y_1$

$\displaystyle y = \frac{14 \times 12}{8} = 21$
Working 9 hours a day, a man completes a job in 8 days. To complete it in 12 days he must work, per day,
A $\displaystyle 10\frac{2}{3}$ hours B $5$ hours C $6$ hours D $13.5$ hours

Answer and solution

Answer: (C) $6$ hours

Inverse proportion: $x_1 y_1 = x_2 y_2$

$8 \times 9 = 12 \times y \Rightarrow y = 6$
$24\%$ as a fraction in its simplest form is
A $\displaystyle \frac{3}{125}$ B $\displaystyle \frac{12}{5}$ C $\displaystyle \frac{3}{25}$ D $\displaystyle \frac{6}{25}$

Answer and solution

Answer: (D) $\displaystyle \frac{6}{25}$

$\displaystyle 24\% = \frac{24}{100} = \frac{6}{25}$
$0.04$ is what percent of $0.8$ ?
A $5\%$ B $0.5\%$ C $20\%$ D $50\%$

Answer and solution

Answer: (A) $5\%$

$\displaystyle \left(\frac{0.04}{0.8} \times 100\right)\% = \left(\frac{4}{80} \times 100\right)\% = 5\%$
The price of a book rises from ₹360 to ₹450. The percentage increase is
A $90\%$ B $20\%$ C $25\%$ D $125\%$

Answer and solution

Answer: (C) $25\%$

Change $= 90$

$\displaystyle \left(\frac{90}{360} \times 100\right)\% = 25\%$

Always divide by the original value.
If $x$ is 4 times $y$ , then $y$ is less than $x$ by
A $25\%$ B $75\%$ C $300\%$ D $400\%$

Answer and solution

Answer: (B) $75\%$

$y = k$ , $x = 4k$ : $\displaystyle \left(\frac{3k}{4k} \times 100\right)\% = 75\%$
The present population of a town is 17280. If it increased at $20\%$ per annum, its population 2 years ago was
A $12{,}000$ B $10{,}368$ C $14{,}400$ D $11059.2$

Answer and solution

Answer: (A) $12{,}000$

$\displaystyle \frac{17280}{\left(1 + \frac{20}{100}\right)^2} = 17280 \times \frac{5}{6} \times \frac{5}{6} = 12000$
The profit made by selling an article for ₹845 is equal to the loss made by selling it for ₹715. The cost price is
A ₹780 B ₹65 C ₹1560 D ₹130

Answer and solution

Answer: (A) ₹780

$845 - x = x - 715 \Rightarrow 2x = 1560 \Rightarrow x = 780$
An article marked at ₹1250 is sold for ₹1000. The discount percent is
A $25\%$ B $12.5\%$ C $80\%$ D $20\%$

Answer and solution

Answer: (D) $20\%$

Discount $= 250$

Discount $\displaystyle \% = \frac{250}{1250} \times 100 = 20\%$ (always on M.P)
A trader claims to sell sugar at cost price but gives only 875 g for every kg. His gain percent is
A $12.5\%$ B $\displaystyle 14\frac{2}{7}\%$ C $\displaystyle 114\frac{2}{7}\%$ D $87.5\%$

Answer and solution

Answer: (B) $\displaystyle 14\frac{2}{7}\%$

Gain $\displaystyle \% = \frac{\text{Error}}{\text{True value} - \text{Error}} \times 100$

$\displaystyle = \frac{125}{875} \times 100 = 14\frac{2}{7}\%$
If the cost price of 12 articles equals the selling price of 16 articles, then there is a
A $25\%$ gain B $\displaystyle 33\frac{1}{3}\%$ gain C $25\%$ loss D $\displaystyle 33\frac{1}{3}\%$ loss

Answer and solution

Answer: (C) $25\%$ loss

$\displaystyle 12x = 16y \Rightarrow \frac{y}{x} = \frac{3}{4}$

$\displaystyle \left(\frac{y}{x} - 1\right) \times 100 = -25\%$ (negative, so a loss)
The average score of a cricketer in 3 matches is 40 and in 2 other matches is 25. His average in all 5 matches is
A $170$ B $34$ C $30$ D $32.5$

Answer and solution

Answer: (B) $34$

Total $= 3(40) + 2(25) = 120 + 50 = 170$

Average $\displaystyle = \frac{170}{5} = 34$
The average of 8 numbers is 14. If each number is multiplied by 3, the new average is
A $14$ B $42$ C $17$ D $336$

Answer and solution

Answer: (B) $42$

Average of $ax_i$ is $a\bar{x}$ : $3 \times 14 = 42$
$22$ m/s in km/h is
A $79.2$ B $\displaystyle 6\frac{1}{9}$ C $7.92$ D $220$

Answer and solution

Answer: (A) $79.2$

$\displaystyle 22 \times \frac{18}{5} = \frac{396}{5} = 79.2$ km/h
A man goes to a place at 36 km/h and returns by the same route at 45 km/h. His average speed for the whole journey is
A $40.5$ km/h B $81$ km/h C $40$ km/h D $42$ km/h

Answer and solution

Answer: (C) $40$ km/h

$\displaystyle \frac{2 \times 36 \times 45}{36 + 45} = \frac{3240}{81} = 40 \text{ km/h}$

(Not the simple average of the two speeds.)
A car takes half the time taken by a truck for the same journey. The truck takes 24 hours. If the car's speed is 110 km/h, the speed of the truck is
A $220$ km/h B $55$ km/h C $165$ km/h D $110$ km/h

Answer and solution

Answer: (B) $55$ km/h

$s_{car} : s_{truck} = T_{truck} : T_{car} = 2 : 1$

Truck speed $\displaystyle = \frac{110}{2} = 55$ km/h
A train 150 m long running at 72 km/h crosses a platform 250 m long in
A $12.5$ seconds B $\displaystyle 5\frac{5}{9}$ seconds C $7.5$ seconds D $20$ seconds

Answer and solution

Answer: (D) $20$ seconds

Distance $= 150 + 250 = 400$ m; speed $\displaystyle = 72 \times \frac{5}{18} = 20$ m/s

$\displaystyle T = \frac{400}{20} = 20$ s
The amount on ₹2000 at $7.5\%$ per annum simple interest for 2 years is
A ₹2311.25 B ₹2300 C ₹2150 D ₹300

Answer and solution

Answer: (B) ₹2300

$\displaystyle \text{S.I} = \frac{2000 \times 2 \times 7.5}{100} = 300$

Amount $= 2000 + 300 = 2300$
The compound interest on ₹5000 at $6\%$ per annum for 2 years, compounded annually, is
A ₹5618 B ₹618 C ₹636 D ₹600

Answer and solution

Answer: (B) ₹618

$\displaystyle A = 5000\left(\frac{53}{50}\right)^2 = 5618$

C.I $= 5618 - 5000 = 618$

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MCQ test, Set 2